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You do not have to mount the PJ at the very back of the room, unless you were planning on shelf mounting it flush against the wall. I don't see that room as being a problem. Without knowing your budget, the two projectors you might look at are the Epson 5010 and the JVC RS-45 (or the newer JVC's which are due out for shipping around XMAS to late Jan).
You did not specify your anticipated screen size or budget, so the question cannot be answered. There are not that many long-throw projectors that do 3D, but I do not think you need a long throw, some of the really expensive 3D ones might have interchangeable lenses (Runcos, Sim3D ones), but after buying the PJ and the lens we are probably talking over $10,000. I know some of the older Optomas (hd8600) also had an interchangeable lens, but these are not 3D and I don't think any of the newer Optomas with 3D had an intechangeable throw lens.
Overall, from the top of my head, the Epson 5010 for under $3000 is able to produce the smallest images from the longest throws (about 25 feet back it can do an image as small as 120"). Also keep in mind this is from the lens, so the projector itself will stick out another 1 foot or so from the mounting position.
You might also consider the JVC's since they can do a 120" image from about 24' back from the lens, and they are even bigger projectors.